Estimating topological properties of weighted networks from limited information

A fundamental problem in studying and modeling economic and financial systems is represented by privacy issues, which put severe limitations on the amount of accessible information. Here we introduce a novel, highly nontrivial method to reconstruct the structural properties of complex weighted networks of this kind using only partial information: the total number of nodes and links, and the values of the strength for all nodes. The latter are used as fitness to estimate the unknown node degrees through a standard configuration model. Then, these estimated degrees and the strengths are used to calibrate an enhanced configuration model in order to generate ensembles of networks intended to represent the real system. The method, which is tested on real economic and financial networks, while drastically reducing the amount of information needed to infer network properties, turns out to be remarkably effective$-$thus representing a valuable tool for gaining insights on privacy-protected socioeconomic systems.